Water Heating System

ABSTRACT

A method, including: receiving an instruction from a user of a hot water tank ( 24 ) indicating a target temperature and a duration of a supply of water. In response to receiving the instruction, water at multiple different temperatures within the hot water tank is mixed so as to form mixed water in the tank. The method includes measuring an actual temperature of the mixed water in order to make a determination of whether the mixed water will satisfy the instruction. The method also includes activating a heater ( 120 ) to heat the mixed water responsively to the determination.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Patent Application 61/242,812, filed 16 Sep. 2009, which is incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates generally to water heating, and specifically to heating of water within a tank.

BACKGROUND OF THE INVENTION

A hot water tank is typically used in a household, as part of the water supply of the household, for supplying hot water for showering, washing, and other domestic uses. A hot water tank may also be used in commercial and industrial applications, in a similar configuration, or optionally modified configurations, to that used in a household. The hot water tank typically receives water from a cold water supply, and heats the received cold water.

Japanese Patent Application 58-130932, to Kubota et al., whose disclosure is incorporated herein by reference, is claimed to relate to a hot water storage-type water heater such as an electrical storage-type water heater.

Japanese Patent Application 2006-046713 to Satou et al., whose disclosure is incorporated herein by reference, is claimed to display an amount of mixed warm water from a hot water storage tank when the water is being used.

The description above is presented as a general overview of related art in this field and should not be construed as an admission that any of the information it contains constitutes prior art against the present patent application.

SUMMARY OF THE INVENTION

An embodiment of the present invention provides a method, including:

receiving an instruction from a user of a hot water tank indicating a target temperature and a duration of a supply of water;

in response to the instruction, mixing water at multiple different temperatures within the hot water tank so as to form mixed water therein;

measuring an actual temperature of the mixed water in order to make a determination of whether the mixed water will satisfy the instruction; and

activating a heater to heat the mixed water responsively to the determination.

Typically, making the determination includes evaluating a heat loss factor of a temperature drop from the hot water tank to a water outlet supplying the user, and incorporating the heat loss factor in the determination.

Alternatively, making the determination includes measuring a temperature of a cold water supply to the user, and incorporating the temperature in the determination.

Further alternatively, making the determination includes making an evaluation if the mixed water is to be heated, and in response to the evaluation presenting a query to the user whether the mixed water is to be heated. Activating the heater may be in response to a positive response to the query.

Typically, activating the heater includes determining that a volume of water to be delivered to the user is less than or equal to a capacity of the hot water tank and that an effective temperature of water from the hot water tank is less than the target temperature.

Alternatively, activating the heater includes determining that a volume of water to be delivered to the user is equal to a capacity of the hot water tank and that the volume of water is at a maximum operating temperature of the tank.

Further alternatively, activating the heater includes determining that a volume of water to be delivered to the user is greater than or equal to a capacity of the hot water tank, and is less than a maximum volume of water to be delivered to the user at the target temperature.

Yet further alternatively, making the determination includes determining that a maximum heat capacity of water in the tank is insufficient for satisfying the instruction, and in response determining a length of time required to heat water entering the tank.

There is further provided, according to an embodiment of the present invention, apparatus, including:

a hot water tank;

a first vertical array of heaters deployed within the hot water tank;

a second vertical array of temperature sensors deployed within the hot water tank; and

a control unit which is configured:

to receive an instruction from a user of the hot water tank indicating a requirement of a supply of water,

to receive signals from the temperature sensors representative of respective temperatures thereof, and

to activate at least one of the heaters in response to the signals and the requirement.

Typically, the first vertical array of heaters are located according to a first vertical distribution and the second vertical array of sensors are located according to a second vertical distribution.

The second vertical distribution may be equal to the first vertical distribution. In one embodiment the first vertical array includes three heaters and the second vertical array includes three sensors, and the three heaters divide the hot water tank into three equal volumes.

Alternatively, the second vertical distribution may be different from the first vertical distribution.

Typically, the control unit is configured to activate the at least one of the heaters in response to evaluating a heat loss factor of a temperature drop from the hot water tank to a water outlet supplying the user.

In one embodiment, the control unit is configured to activate the at least one of the heaters in response to measuring a temperature of a cold water supply to the user.

In a disclosed embodiment, the control unit is configured to activate the at least one of the heaters in response to receiving a positive response to a query to the user whether water within the hot water tank is to be heated.

Typically, the instruction is indicative of a temperature and a volume of the supply of water.

In an alternative embodiment the control unit is configured to activate the at least one of the heaters in response to analyzing sequentially heat contents of respective sections of the tank defined by the first vertical array.

In a further alternative embodiment the first vertical array defines respective sections of the tank, and the control unit is configured to activate the at least one of the heaters in response to maintaining that no given section is heated to a first temperature that is higher than a second temperature of a further section above the given section.

Typically, the instruction includes determining that a maximum heat capacity of water in the tank is insufficient for satisfying the instruction, and in response determining a length of time required to heat water entering the tank.

There is further provided, according to an embodiment of the present invention, apparatus, including:

a hot water tank;

a heater within the hot water tank;

a pump coupled to the hot water tank; and

a control unit, which is configured to receive an instruction from a user of the hot water tank indicating a target temperature and a duration of a supply of water;

in response to the instruction, activate the pump to mix water at multiple different temperatures within the hot water tank so as to form mixed water therein;

measure an actual temperature of the mixed water in order to make a determination of whether the mixed water will satisfy the instruction; and

activate the heater to heat the mixed water responsively to the determination.

There is further provided, according to an embodiment of the present invention, a method, including:

deploying a first vertical array of heaters within a hot water tank;

deploying a second vertical array of temperature sensors within the hot water tank; and

configuring a control unit:

to receive an instruction from a user of the hot water tank indicating a requirement of a supply of water,

to receive signals from the temperature sensors representative of respective temperatures thereof, and

to activate at least one of the heaters in response to the signals and the requirement.

There is further provided, according to an embodiment of the present invention, a method, including:

receiving a first instruction from a first user of a hot water tank indicating a first requirement of a first supply of water;

in response to the first instruction, mixing water at multiple different temperatures within the hot water tank so as to form mixed water therein;

measuring an actual temperature of the mixed water in order to make a determination of whether the mixed water will satisfy the first instruction;

activating a heater to heat the mixed water responsively to the determination;

while the first requirement is being met, receiving a second instruction from a second user of the hot water tank indicating a second requirement of a second supply of water; and

making a determination of whether the mixed water will satisfy the second requirement.

There is further provided, according to an embodiment of the present invention, apparatus, including:

a hot water tank;

a first vertical array of heaters deployed within the hot water tank;

a second vertical array of temperature sensors deployed within the hot water tank; and

a control unit which is configured:

to receive respective instructions from two or more users of the hot water tank indicating respective requirements of supplies of water,

to receive signals from the temperature sensors representative of respective temperatures thereof, and

to activate at least one of the heaters in response to the signals and the respective requirements.

There is further provided, according to an embodiment of the present invention, apparatus, including:

a hot water tank;

a heater within the hot water tank;

a pump coupled to the hot water tank; and

a control unit, which is configured to receive a first instruction from a first user of the hot water tank indicating a first requirement of a first supply of water;

in response to the first instruction, activate the pump to mix water at multiple different temperatures within the hot water tank so as to form mixed water therein;

measure an actual temperature of the mixed water in order to make a determination of whether the mixed water will satisfy the first instruction;

activate the heater to heat the mixed water responsively to the determination;

while the first requirement is being met, receive a second instruction from a second user of the hot water tank indicating a second requirement of a second supply of water; and

make a determination of whether the mixed water will satisfy the second requirement.

There is further provided, according to an embodiment of the present invention, a method, including:

deploying a first vertical array of heaters within a hot water tank;

deploying a second vertical array of temperature sensors within the hot water tank; and

configuring a control unit:

to receive respective instructions from two or more users of the hot water tank indicating respective requirements of supplies of water,

to receive signals from the temperature sensors representative of respective temperatures thereof, and

to activate at least one of the heaters in response to the signals and the respective requirements.

The present invention will be more fully understood from the following detailed description of the embodiments thereof, taken together with the drawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of the operation of a water heating system, according to an embodiment of the present invention;

FIGS. 2A, 2B, and 3 are respectively first, second and third block diagrams illustrating the components of the system of FIG. 1, according to an embodiment of the present invention;

FIG. 4 is a flow chart describing steps that are implemented in operation of the system of FIG. 1, according to an embodiment of the present invention:

FIGS. 5A, 5B, and 6 are respectively first, second and third block diagrams illustrating the components of an alternative water heating system, according to an embodiment of the present invention;

FIG. 7 is a flow chart describing steps that are implemented in operation of the alternative water heating system, according to an embodiment of the present invention; and

FIGS. 8A-8N illustrate a flow chart followed by a processing unit in making its decisions in steps of the flow chart of FIG. 7, according to an embodiment of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS Overview

Embodiments of the present invention seek to provide methods and apparatus for efficient heating of hot water in a water supply system. The water supply system comprises a hot water tank and a cold water supply. Water from the tank and from the cold water supply may be mixed by a user to generate water for the user. In the system the user is able to input, as instructions giving user requirements, a target (user) temperature for supply of the water. Once the instructions have been received, the system calculates, typically immediately, one or more temperatures to which water in the tank is to be heated to supply the requirements, and activates one or more heaters to heat the water to the calculated temperatures. Typically, a display unit provides indications to the user how much water (mixed) is immediately available, or whether water in the tank needs to be heated to satisfy the user requirements. In some embodiments the instructions comprise a required duration of supply of the water, and the required duration may be incorporated into the calculation of the one or more temperatures.

In one embodiment having a mixing pump, on receipt of the user instructions, the water in the tank is immediately mixed by the pump. Typically, absent mixing, water in a hot water tank stratifies so that a hot water layer is above a cold water layer. The mixing causes the different temperature water layers to homogenize, so that all the water in the tank is at one temperature. A control unit then measures the temperature, and determines if the mixed water (in the tank) will satisfy the user instructions, typically after being heated, or typically after being mixed with water from the cold water supply.

In an alternative embodiment, there is no mixing pump. Thus water in the tank typically remains stratified. The alternative embodiment comprises an array of heaters deployed vertically, and an array of temperature sensors that are also deployed vertically. In an exemplary embodiment there are three heaters and three sensors, deployed so as to approximately divide the tank into three equal sections, one above the other. On receipt of the user instructions, the control unit measures the water temperatures in the stratified sections of the tank, and determines if one or more of the heaters in the tank are to be activated to satisfy the user requirements. The heaters are activated in such a way so that the stratification is typically maintained.

DETAILED DESCRIPTION

Reference is now made to FIG. 1, which is a schematic illustration of the operation of a water heating system 20, according to an embodiment of the present invention. In FIG. 1 system 20 is shown, by way of example, to be used to heat water for a shower 22 in a dwelling. However, it will be understood that embodiments of the present invention are not limited to such a use, but rather may be used wherever a partially or completely heated water supply is operative.

System 20 comprises a hot water storage tank 24, wherein water that is to be used in the shower is stored. Tank 24 is connected by piping 25 to a mixing faucet 26 and a shower head 28 within the shower, and the faucet is operated by a user (not shown) of the shower to control the flow of water to the shower head. System 20 also comprises a control unit 30, which enables the user to operate the system. Control unit 30 allows the user to input data to the system via a data input device 32, which is assumed herein, by way of example, to comprises a keypad, although the data input device may use any other convenient mechanism, such as a touchpad and/or switches, to input data.

Control unit 30 also comprises a data output device 34, which provides output information to the user of system 20. Data output device 34 is assumed herein, by way of example, to comprise an LCD (liquid crystal display) screen so that the device is also referred to herein as display 34. However, it will be understood that the device may comprise another type of visual display, and/or an auditory output device, and those having ordinary skill in the art will be able to adapt the description, mutatis mutandis, for output devices other than an LCD.

The elements of system 20, and their method of operation, are described in more detail below with respect to FIGS. 2A, 2B, and 3.

FIGS. 2A, 2B, and 3 are respectively first, second and third block diagrams illustrating the components of system 20, according to an embodiment of the present invention. As illustrated in FIG. 2A, control unit 30 comprises a processing unit 102, which operates system 20, and which typically comprises a processor 103 coupled to a memory 105, wherein are stored operating instructions for the processor. Processing unit 102 may be implemented from “off-the-shelf” components, custom-built components, or a combination of off-the-shelf and custom-built components. In some embodiments processing unit 102 may comprise a field programmable gate array (FPGA) and/or an application specific integrated circuit (ASIC). Memory 105 typically comprises volatile and/or non-volatile memories. In one embodiment unit 102 comprises an M91-2-UN2 unit produced by Unitronics Inc, of Quincy, Mass.

Processing unit 102 communicates with other elements of system 20 by cable, which may comprise wired and/or optical cable, and/or by wireless. Herein, by way of example, the processing unit is assumed to communicate by wireless with at least some of the other elements of system 20 using a transceiver 110. For simplicity, respective transceivers in the elements of system 20 which are in communication with transceiver 110 are not shown in the diagrams.

A power supply 104 in control unit 30 supplies power to processing unit 102, to data input device 32, to data output device 34, to transceiver 110, and to other elements of system 20, such as valves 118, 129, 131, and a pump 127, described further below. The power supply may be battery and/or line operated.

FIG. 3 schematically illustrates elements of system 20 that are in communication with control unit 30. Tank 24 is typically an off-the-shelf insulated tank constructed to hold and supply hot water. In one embodiment tank 24 has a volume between 75 and 300 US gallons. The tank is fed from a cold water supply via an inlet pipe 113, wherein there is a cold water inlet valve 129. Valve 129 is controlled by control unit 30, and under instructions from the unit may be in either an open state or a closed state. Pipe 113 in turn connects to a tube 113B within tank 24. Tube 113B terminates close to the interior bottom of tank 24, so that if valve 129 is open cold water may enter the tank at a low point in tank 24.

A cold water temperature sensor 112 is typically connected to pipe 113, so as to provide a measure of the temperature of the cold water supply to unit 30. Cold water sensor 112 may comprise a thermistor, or any other convenient temperature measuring device having a characteristic from which unit 30 is able to derive the temperature of the cold water supply.

In some embodiments sensor 112 comprises a multiplicity of generally similar temperature sensors respectively connected to different locations of the cold water supply. Such embodiments may be implemented in the case of, for example, a residence where the temperature within the residence may be higher than the temperature of the external water supply to the residence. Typically, in the case of a plurality of temperature sensors, the lowest temperature reading of the sensors is used by control unit 30 as a cold water temperature value Tc in any calculations involving Tc. Cold water temperature Tc, and calculations involving the cold water temperature, are described further below.

In some embodiments more than one water heating system 20 may be installed, for example in a building comprising a group of apartments. In such an installation it will be appreciated that, since the multiple systems are fed by a common cold water supply, a single sensor 112 may be used for the multiple water heating systems.

In system 20, located close to the bottom of the tank, a heater 120 is installed in tank 24. The heater may be switched on or off, under control of unit 30, by a heater switch 124. Heater 120 typically comprises an electrical resistor which is connected, via switch 124, to the line supply. Alternatively, heater 120 may generate its heat non-electrically. For example, the heater may be operated by gas. While heater 120 typically comprises one heating element, it may comprise two or more separate elements. A tank water temperature sensor 114 is also installed close to the bottom of tank 24, to provide a measure of the temperature of water at the tank bottom to unit 30. Tank water sensor 114 is typically similar to sensor 112, described above.

The hot water outlet from tank 24 comprises an outlet pipe 111 that is connected to the upper internal surface of the tank, so that hot water from the tank exits from an upper portion of the tank. A hot water outlet valve 118, controlled to be open or closed by unit 30, is connected in pipe 111. After valve 118 pipe 111 is connected to a hot water inlet of mixing faucet 26.

A pump 127, controlled by unit 30, connects, via a coupling pipe 128, inlet pipe 113 and outlet pipe 111. As is shown in FIG. 3, pipe 128 is implemented to connect to the inlet pipe and the outlet pipe below valve 129 and valve 118 respectively. Activation of pump 127 by unit 30 initiates transfer of water between the inlet and outlet pipes. If the pump is deactivated by unit 30, the pump acts to prevent water transfer between the inlet and outlet pipes.

A pipe 113A connects the cold water supply to a cold water inlet of mixing faucet 26. In pipe 113A there is an on/off valve 131, the state of the valve being controlled by unit 30.

In some embodiments a flow sensor 130 is connected in the outlet of mixing faucet 26. Sensor 130 provides signals to unit 30 enabling the unit to calculate a rate of flow of water from the faucet.

FIG. 2B schematically illustrates processing unit 102 in more detail. As stated above, unit 102 comprises processor 103 and memory 105. Memory 105 comprises a number of modules, as listed below. The modules may be implemented in software, hardware, or a combination of software and hardware.

An available-time module 513. Module 513 enables the processor to calculate a time period (length of time) Ma within which mixed water is available to the system user.

A maximum-time module 514. Module 514 enables the processor to calculate a maximum time period (length of time) Mm for which mixed water is available to the system user.

A required-(tank) temperature module 515. Module 515 enables the processor to calculate a required temperature Tr of water in tank 24, that is needed in order to meet user requirements (required-time).

A difference-time module 516. Module 516 enables the processor to calculate a difference between a required-time which is greater than the maximum-time and the maximum-time.

An optional flow rate module 517 for calculating a faucet flow rate.

A real time clock module 519 that provides time signals to the processor.

In addition to the modules listed above, memory 105 typically comprises a general memory region 520 that processor 103 is able to use during operation of system 20. Region 520 is typically used, inter alia, to store system parameters, such as the volume of tank 24, a set point temperature and the like, that are used by the processor in performing its calculations.

FIG. 4 is a flow chart describing steps that are implemented in operation of system 20, according to an embodiment of the present invention. Except where otherwise indicated, the following description of the flow chart assumes an embodiment wherein flow sensor 130 and flow rate module 517 are not present, and that the flow rate from faucet 26 is Fr.

In a system installation step 600, operational parameters of the system are input to unit 30, which typically stores the parameters in memory region 520. A technician typically performs step 600 using data input device 32, although any other convenient method for inputting the parameters, such as via transceiver 110, may be used. Parameters which are stored in step 600 comprise:

-   -   A set point temperature, Ts, for tank 24. When the measured         temperature of the water in the tank reaches Ts, the activation         of the heater is stopped automatically by unit 30, which limits         the temperature to a maximum tank operating temperature Ts, the         set point temperature, to which water in the tank may be heated.         The value of set point temperature Ts may be set in production         of tank 24, or alternatively at initial installation of the         tank. A typical value for Ts is approximately 140° F. (60° C.).     -   A set time of operation, Po, of pump 127. As described in more         detail below, pump 127 is used to mix the water in tank 24.         However, the mixing only needs to be performed for a limited         period of time, Po, until the temperature of the water in the         tank is substantially uniform. Those having ordinary skill in         the art will be able to determine a value of Po without undue         experimentation, for example by observing values of temperature         registered by sensor 114 while the water in the tank is being         mixed.     -   An output flow rate, Fr, of mixing faucet 26. The output flow         rate of the faucet may be measured, by methods which are well         known in the art, such as by determining the volume of water         flowing from the faucet in a measured time interval.         Alternatively, a value of Fr may be determined from         manufacturer's data, or from a plumbing code such as the Uniform         Plumbing Code published by the International Association of         Plumbing and Mechanical Officials (IAPMO), Ontario CA. A typical         value for Fr is in the range of 1-3 US gallons/minute.     -   A capacity, Ct, of tank 24. The capacity is typically in the         range of 75-300 US gallons.     -   A heat loss rate factor Lr. Factor Lr is a dimensionless number,         0<Lr≦1, which is a measure of the temperature drop from tank 24         to the hot water inlet of faucet 26. An equation (1) defines Lr:

$\begin{matrix} {{Lr} = \frac{T_{faucet}}{T_{tank}}} & (1) \end{matrix}$

where T_(faucet) is the temperature of the water at the hot water inlet of the faucet, and T_(tank) is the temperature of the water exiting from tank 24.

-   -   The value of Lr depends on factors such as the length of piping         between tank 24 and shower 22 and the quality of insulation on         the piping. Typically the value of Lr is close to unity, and an         actual value may be determined by measuring values of T_(faucet)         (the hot water inlet of the faucet) and T_(tank).

In a user step 601, the user inputs a user desired target temperature, Tu, using input device 32. The value of Tu input by the user is typically confirmed by display 34.

In a cold water temperature measuring step 602, processing unit 102 samples signals from sensor 112, and converts the signals to a cold water temperature value, Tc. Tc is the temperature of the cold water inlet to faucet 26 and to tank 24. The sampling is typically performed in response to the start of operations of the user in step 601, and may also be performed at other times, continuously or intermittently, during operation of system 20.

In a temperature equalization step 603, typically performed in response to the start of user operations in step 601, processing unit 102 sends signals for closing valves 118 and 129. Once the valves have closed, the processing unit sends a signal to activate pump 127 for its set time of operation Po, using real time clock module 519.

By closing valves 118 and 129, pump 127 acts as a water mixing pump, extracting warm water from the upper outlet of tank 24 and injecting it via pipe 113B into the lower part of the tank, so that water that is initially at different temperatures in the tank is mixed. At the conclusion of time Po, the processing unit sends a signal to deactivate the pump, so that the pump acts to prevent water traversing coupling pipe 128; the processing unit also sends signals for opening valves 118 and 129.

In a temperature measuring step 604, performed at the conclusion of time Po, processing unit 102 determines a measured actual temperature Tt of the mixed water in tank 24 by sampling signals from sensor 114. The processing unit converts temperature Tt to an effective temperature Te at the hot water inlet of faucet 26, using the heat loss factor Lr, according to equation (2):

Te=Tt·Lr   (2)

In a first comparison 605, the processing unit compares Te(Tt·Lr) and Tu. If Te<Tu, processing unit continues to a display step 608. If Te≧Tu, the processing unit continues to a calculation step 606.

In calculation step 606 the processing unit uses available-time module 513 to calculate an available time interval (length of time) Ma during which mixed water may exit from faucet 26 at temperature Tu. The calculation performed with the module is based on the law of conservation of energy, and uses equation (3):

$\begin{matrix} {{Ma} = \frac{{Ct} \cdot \left( {{Te} - {Tc}} \right)}{{Fr} \cdot \left( {{Tu} - {Tc}} \right)}} & (3) \end{matrix}$

For example, in the preceding steps of the flow chart the following values may be determined: Ct=75 gallons; Tu=100° F.; Tc=50° F.; Fr=2.5 gallons/minute; Tt=110° F.; and Lr=1 (the last equality assumes there is negligible heat loss in the system). Applying these values to equations (2) and (3) gives a value of Ma of 36 minutes (i.e., 36 minutes of water supplied to the user at 100° F.).

In a data output step 607, the processing unit presents the value calculated in step 606 on display 34.

In display step 608 (which follows from a return of Te<Tu in comparison 605), display 34 shows, on instructions from the processing unit, that there is no mixed water presently available, at Tu, from faucet 26. For example, the display may indicate that Ma=0.

In a second comparison 609, which follows from steps 607 and 608, processing unit 102 uses display 34 to query if the user wants to heat the water in tank 24. If the return from the query is negative, i.e., the water is not to be heated in the tank, the process illustrated by the flow chart ends.

If the return from the query is positive, then in a maximum-time step 610 processing unit 102 uses maximum-time module 514 to calculate a maximum time interval (length of time), Mm, during which the user could receive mixed water at temperature Tu from faucet 26. The calculation is based on assuming that all the water in tank 24 is raised to the maximum set temperature Ts of the tank. The processing unit and the maximum-time module use equation (4) to calculate Mm:

$\begin{matrix} {{Mm} = \frac{{Ct} \cdot \left( {{{Ts} \cdot {Lr}} - {Tc}} \right)}{{Fr} \cdot \left( {{Tu} - {Tc}} \right)}} & (4) \end{matrix}$

For example, using the value of Ts=140° F., and the parameter values given for the numerical example of equation (3) above, Mm=54 minutes.

In a user step 611 the user inputs, to processing unit 102, a length of time required, Mr, for mixed water at temperature Tu (the user required temperature) to be received from faucet 26. The user operates input device 32 to provide the value of Mr to the processing unit. Typically the input is echoed on display 34.

In a third comparison 612 processing unit 102 compares Mr and Mm. If Mr≦Mm, i.e. the user required time is less than or equal to the maximum time that water at the user desired temperature Tu can be provided, so that the system is able to satisfy the user instruction, the flow chart continues to a required temperature calculation step 613. If Mr>Mm, i.e. the user required time is more than the maximum time that water can be provided, so that the system is unable to satisfy the instruction from the user within one cycle of heating, i.e., heating to the set point temperature Ts, the flow chart continues to a heating step 617.

In required temperature calculation step 613, processing unit 102 uses required-temperature module 515 to determine the required temperature Tr to which the water in tank 24 is to be heated. Module 515 stores a number of conditions which the processing unit applies.

A first condition applies if the volume of water to be delivered from faucet 26 is less than or equal to the tank capacity Ct, but the effective temperature Te of the water from the tank is less than the user desired temperature Tu. If this condition is true, then the processing unit sets Te to be at least equal to Tu. Herein, by way of example, Te is assumed to be set equal to Tu. It will be understood that in this case no cold water is required to be mixed at faucet 26, so that typically processing unit 102 sets valve 131 closed.

Applying equation (2), the first condition corresponds to expression (5):

$\begin{matrix} {{{If}\left\{ {{Mr} \leq {\frac{Ct}{Fr}\mspace{14mu} {and}\mspace{14mu} {Te}} < {Tu}} \right\} \mspace{14mu} {then}{\mspace{11mu} \;}{Tr}} \geq \frac{Tu}{Lr}} & (5) \end{matrix}$

A second condition applies if Mr=Mm. In this case the processing unit sets Tr=Ts.

A third condition applies if the volume of water to be delivered from faucet 26 is greater than or equal to the capacity of the tank (to deliver water at the user desired temperature Tu), corresponding to

${Mr} \geq {\frac{Ct}{Fr}.}$

In this case cold water is mixed with the tank hot water at faucet 26 so that processing unit sets valve 131 open, and equation (6) applies:

Mr·Fr·Tu=Ct·Tr·Lr+(Mr·Fr·Ct)Tc   (6)

In equation (6) the left side of the equation is an expression for the total heat energy in the mixed water. On the right side the first term is an expression for the heat energy from the tank, and the second term is an expression for the heat energy from the cold water.

Equation (6) rearranges to give an expression for Tr, as in equation (7):

$\begin{matrix} {{Tr} = \frac{{{Mr} \cdot {Fr} \cdot \left( {{Tu} - {Tc}} \right)} + {{Ct} \cdot {Tc}}}{{Ct} \cdot {Lr}}} & (7) \end{matrix}$

The following two examples illustrate the use of expression (5) and equation (7). The examples assume that Tc=50° F., Ct=75 gpm, and Lr=1 (the values used in step 606).

Example 1: Mr=5 minutes, Te=80° F., Tu=100° F.

Example 2: Mr=33 minutes.

For example 1, the first condition applies so that Tr=Tu=100° F.

For example 2, the third condition applies. Substituting the values for the parameters of equation (7) given in step 606 gives:

${Tr} = {\frac{{33 \cdot 2.5 \cdot \left( {100 - 50} \right)} + {75 \cdot 50}}{75 \cdot 1} = {105{^\circ}\mspace{14mu} {F.}}}$

In a heating step 614 (following from step 613), processing unit 102 sends a signal to switch 124 to activate heater 120, and the processing unit also monitors the tank temperature Tt with sensor 114. The heater is activated and the temperature in the tank is monitored until the required temperature Tr is reached. Tr is derived from step 613. Typically, display 34 provides an indication that the tank is being heated, the value of Tr, and/or an estimate of the length of time needed to reach temperature Tr.

In a deactivation step 615, the processing unit sends a signal to switch 124 to deactivate the heater once the required temperature Tr is reached. Typically, even after deactivating the heater, processing unit 102 continues to monitor the tank temperature, so that if the tank temperature falls below Tr, typically before use of water from the tank, the processing unit may reactivate the heater.

In a display step 616, once temperature Tr has been reached, display 34 indicates to the user that the water in tank 24 has been sufficiently heated to satisfy the user's requirements, i.e., that there is sufficient hot water for faucet 26 to supply water to the user at temperature Tu for a time Mr. The flow chart then ends.

In heating step 617 (which, as stated above, is implemented if in comparison 612 Mr>Mm), processing unit 102 sends a signal to switch 124 to activate heater 120, and the processing unit also monitors the tank temperature Tt with sensor 114. The heater is activated and the temperature in the tank is monitored until the set point temperature Ts is reached. Ts is derived from general memory 520. Typically, display 34 provides an indication that the tank is being heated, the value of Ts, and/or an estimate of the length of time needed to reach temperature Ts using a process similar to that described below for evaluating a required heating time Mh.

In a deactivation step 618, the processing unit sends a signal to switch 124 to deactivate the heater once the set point temperature Ts is reached. Typically, even after deactivating the heater, processing unit 102 continues to monitor the tank temperature, so that if the tank temperature falls below Ts before a use of water from the tank, the processing unit may reactivate the heater.

In a display step 619, once temperature Ts has been reached and even if required-time Mr is unavailable, display 34 indicates to the user that for the time being, the maximum-time Mm is available i.e., that there is sufficient hot water for faucet 26 to supply water to the user at temperature Tu_for a maximum-time Mm.

In a difference time calculation step 620, processing unit 102 uses difference-time module 516 to calculate the difference between the required-time Mr and the maximum-time Mm, assigning the difference to a difference-time Md. Module 516 derives the required-time Mr from processing unit 102 and the maximum-time Mm from module 514. Module 516 uses equation (8) to calculate the difference-time Md:

Md=Mr−Mm   (8)

In a heating time calculation step 621 processing unit 102 uses heating-time module 518 to calculate a required heating-time Mh for activation of heater 120. Heating-time Mh is the time needed, beyond the one cycle of heating as denoted in steps 617 and 618, for meeting the difference-time Md. Heating-time Mh applies if the user requirements lead to exceeding a maximum heat capacity, Ct·Ts, of the tank, so that cold water incoming to the tank requires heating. The calculated heating-time (Mh) is stored in memory unit 105. The calculation of the heating time is based on the law of conservation of energy, and uses equation (9):

$\begin{matrix} {{Mh} = \frac{{{Vd} \cdot \Delta}\; t}{Pt}} & (9) \end{matrix}$

where Vd is a volume of water to be heated, calculated below in equation (10),

Δt is a difference in temperature, calculated below in equation (11), and

Pt is a power of heater 120.

The required volume of water that needs heating, Vd, is determined by comparing the amount of heating required to meet the difference-time Md with the amount of heating required to meet the maximum-time Mm. Vd may be calculated by equation (10):

$\begin{matrix} {{Vd} = \frac{{Ct} \cdot {Md}}{Mm}} & (10) \end{matrix}$

where the terms of the equation are defined above.

Δt is the difference between the set point temperature Ts and the cold water inlet temperature Tc, and is defined by equation 11:

Δt=Ts−Tc   (11)

Applying equations (8), (10), and (11) to equation (9) gives an equation (12) for Mh:

$\begin{matrix} {{Mh} = \frac{{{Ct}\left( {{Mr} - {Mm}} \right)} \cdot \left( {{Ts} - {Tc}} \right)}{{Mm} \cdot {Pt}}} & (12) \end{matrix}$

In step 621 processing unit 102 uses equation (12) to evaluate Mh.

For example, in the preceding steps of the flow chart the following values may be determined: Ct=75 US gallons; Mr=60 minutes; Mm=45 minutes; Ts=140° F.; Tc=50° F.; Pt=40,000 BTU/h (British thermal units per hour). (Using BTU/h the volume in US gallons is converted to pounds by multiplying by 8.3) Applying these values to equations (12) gives a value of Mh of 28 minutes. Thus, to supply the user requirement Mr of 60 minutes, cold water entering tank 24 (to replace hot water leaving the tank) is heated for 28 minutes.

In an activation step 622 processing unit 102 monitors the temperature of the water in the bottom of the tank, Tt, and when it is less than the set point temperature Ts, it activates the heater. The heater is activated continuously or discontinuously, for a total time Mh as measured by R.T.C module 519, according to the flow of water out of (and the corresponding flow of cold water into) tank 24.

In a deactivation step 622 processing unit 102 stops the activation of the heater once heating-time Mh is achieved.

The processing unit then continues to display step 616, described above, and then ends.

The above description of the flow chart assumes that flow sensor 130 is not present. Those having ordinary skill in the art will be able to adapt the description, mutatis mutandis, for embodiments where sensor 130 and flow rate module 517 are present. The sensor provides, in real time, values to the processing unit of the flow rates from faucet 26. In conjunction with real time clock module 519 and flow rate module 517 the processing unit may use these values to derive information useful to the user, and provide this information on display 34. Thus, as well as providing a point in time to the processing unit indicative of the user initially opening faucet 26, the sensor also provides an indication to processing unit 102 that the flow rate is different from Fr. Such a difference, typically a reduction in flow rate from faucet 26, typically leads to a different value for the (required) time Mr, the available time Ma, and the maximum time Mm.

For example, the conditions of example 2 (presented above with reference to step 613) may apply, and the user may operate faucet 26 at a flow rate of Fr (2.5 gpm) for 9 minutes, then adjust the faucet so the flow rate is only 1.5 gpm. In this case, display 34 may show a time period (length of time) for which water at temperature Tu is available. Initially this will be 33 minutes. After 9 minutes (determined by module 519) the available time is 24 minutes at 2.5 gpm, but the processing unit may calculate a new available time, based on the reduced measured flow of 1.5 gpm, equal to 40 minutes and show this time on display 34.

Other applications for sensor 130 will be apparent to those having ordinary skill in the art, and all such applications are assumed to be within the scope of the present invention.

FIGS. 5A, 5B, and 6 are respectively first, second and third block diagrams illustrating the components of a water heating system 300, according to an alternative embodiment of the present invention. Apart from the differences described below, the operation of system 300 is generally similar to that of system 20 (FIGS. 1, 2A, 2B, and 3), and elements indicated by the same reference numerals in both systems 20 and 300 are generally similar in construction and in operation.

As shown in FIG. 5B, memory 105 does not comprise required-temperature module 515. However, in addition to the other modules described above with reference to FIG. 2B, memory 105 comprises further modules, as listed below. The modules may be implemented in software, hardware, or a combination of software and hardware.

-   -   An average-temperature module 711. Module 711 enables the         processor to calculate an average effective temperature Ta of         all or part of the water in the tank.     -   A currently-available-volume module 712. Module 712 enables the         processor to calculate an available volume of hot water Ca in         terms of the volume Ct of tank 24.     -   A required-temperature module 715. Module 715 differs from         module 515 of system 20 in that module 715 is configured to         calculate required temperatures Tr1, Tr2, Tr3, of different         sections of tank 24, and/or a required average temperature Tr of         the tank. Temperatures Tr1, Tr2, Tr3, and Tr are described         further below.

As shown in FIG. 6, in system 300 there is no pump 128, and there is no connecting pipe 128 between cold water inlet pipe 113 and outlet pipe 111. There is no valve 129 in the cold water inlet pipe, although in some embodiments of system 300 valve 118 is present (with a different function, as explained below, from the function in system 20). In tank 24, in addition to heater 120 and its associated switch 124, there are two more heaters 321, 322, with respective associated switches 325, 326. Heaters 321, 322, and switches 325, 326 are typically similar in construction and function to heater 120 and switch 124, described above. As shown in FIG. 5A, all heater switches are under control of processing unit 102.

In addition to sensor 114, which is assumed to provide a temperature measurement T1, tank 24 has two extra temperature sensors 315, 316, respectively approximately level with heaters 321, 322. The tank may optionally have a further temperature sensor 317 located close to the top of the tank. All sensors are typically generally the same in function and construction. Sensors 315, 316, and 317 are assumed to provide respective temperature measurement T2, T3, and T4. FIG. 5A illustrates that all temperature sensors provide their temperature related signals to unit 102.

As stated above, heater 120 and sensor 114 are located close to the bottom of tank 24. In an exemplary embodiment described herein heater 321 and sensor 315 are located approximately one third of the way up the tank, and heater 322 and sensor 316 are located approximately two thirds of the way up the tank. In embodiments of the present invention the heaters are deployed in the tank in a heater vertical array, and the sensors are deployed in a sensor vertical array. In the exemplary embodiment described herein, the heater vertical array and the sensor vertical array have substantially the same vertical distribution, i.e., the vertical location of the elements of the arrays are substantially the same, so that there are three heaters and three sensors which effectively divide the tank into three approximately equal volumetric sections V1, V2, and V3.

Typically, since there is little diffusion in the tank, and since hot water is less dense than cold water, the three sections typically form three different strata of water, which have little or no mixing. Thus, as is assumed in the description herein, and since the sensors are at the bottom of their respective sections, the upper water layer typically has a temperature approximately equal to or higher than T3, the middle water layer typically has a temperature approximately equal to or higher than T2, and the lower water layer typically has a temperature approximately equal to or higher than T1, where T3>T2>T1.

As explained in more detail below, embodiments of the present invention provide a method for calculating and implementing respective required temperatures Tr1, Tr2, and Tr3 of sections V1, V2, and V3.

While the following description assumes the configuration of three heaters and sensors described above, it will be understood that embodiments of the present invention comprise other arrays of heaters and arrays of sensors, such as 2, 4, or more heaters and 2, 4, or more sensors. While typically there may be equal numbers of heaters and sensors, this is not a requirement for embodiments of the invention, and the numbers may be different. For example, there may be three heaters and four sensors, and values from the sensors may be interpolated to determine the temperatures of the strata defined by the heaters.

It will also be understood that the arrangements of the heaters and/or sensors does not need to divide the tank into equal sections, so that some embodiments may have sections, and corresponding water layers, with different volumes. The choice herein of the tank with three heaters and sensors arranged to divide the tank equally is purely to clarify the explanation, and those having ordinary skill in the art will be able to adapt the description, mutatis mutandis, for systems with a different number of heaters from three, and a different number of sensors from three, the heaters and sensors being equal or different in number from each other, and/or where at least some of the layers defined by the vertical array of heaters are unequal in volume.

FIG. 7 is a flow chart describing steps that are implemented in operation of system 300, according to an embodiment of the present invention. Except where otherwise indicated, the following description of the flow chart assumes an embodiment wherein flow sensor 130 and flow rate module 517 are not present and that the flow rate from faucet 26 is Fr, wherein valve 118 is not present, and wherein sensor 317 is not present.

A system installation step 900 is substantially the same as installation step 600 described above, except that there is no measurement of the time of operation, Po, of pump 127.

A user step 901 and a cold water temperature measuring step 902 are substantially the same as respective steps 601, 602, described above, providing a user required temperature Tu and a cold water inlet temperature Tc, described above.

In a section temperature measuring step 903, processing unit 102 samples signals from sensors 114, 315, 316, and converts the signals to temperatures T1, T2, T3 of respective sections V1, V2, and V3. The sampling is typically performed in response to the start of operations of the user in step 901, and may also be performed at other times, continuously or intermittently, during operation of system 20. The processing unit converts temperatures T1, T2, T3 to respective effective temperatures T1 e, T2 e, T3 e at the hot water inlet of faucet 26, using the heat loss factor Lr, according to equation (13):

Tne=Tn·Lr   (13)

where n=1, 2, or 3.

In a first comparison 904, the processing unit compares the values of T1 e, T2 e, T3e with Tu. If all of T1 e, T2 e, T3 e are less than Tu, i.e., if T1 e<Tu AND T2 e<Tu AND T3 e<Tu, the processing unit continues to a display step 909. Otherwise, the processing unit continues to an average temperature step 905.

In average temperature step 905, the processing unit uses average-temperature module 711 to calculate an average effective temperature Ta of sections of tank 24 that have effective temperatures greater than Tu. Herein, by way of example, the average calculated is assumed to comprise an arithmetic mean. However, other averages, such as a geometric mean or a harmonic mean may be used.

For example, T3 e and T2 e may both be greater than Tu, but T1 e may be less than Tu. In this case the processing unit calculates Ta as

$\frac{{T\; 3e} + {T\; 2\; e}}{2}.$

If only T3 e is greater than Tu, Ta=T3 e. If T3 e, T2e, and T1 e are all greater than Tu, the processing unit calculates Ta as

$\frac{{T\; 3e} + {T\; 2\; e} + {T\; 1e}}{2}.$

In a hot water volume step 906 the processing unit uses currently-available-volume module 712 to calculate an available volume Ca of hot water, i.e., the volume of hot water in tank 24 that has an effective temperature greater than or equal to Tu. Ca may be 1/3Ct, 2/3C_(t) or Ct, according to whether only section V3, sections V3 and V2, or all sections V3, V2, and V1 have effective temperatures greater than or equal to Tu.

In an available mixed water step 907, processing unit 102 uses the results from steps 905 and 906 to calculate a time period (length of time) Ma that mixed water at temperature Tu may be provided from faucet 26. Equation (14), which has the same structure as equation (6), applies:

Ma·Fr·Tu=Ca·Ta+(Ma·Fr−Ca)·Tc   (14)

Equation (14) rearranges to an equation (15) for Ma:

$\begin{matrix} {{Ma} = \frac{{Ca}\left( {{Ta} - {Tc}} \right)}{{Fr}\left( {{Tu} - {Tc}} \right)}} & (15) \end{matrix}$

For example, in the initial steps of the flow chart the following values may be determined: Ct=75 gallons; Tu=100° F.; Tc=50° F.; Fr=2.5 gallons/minute; T1=100° F.; T2=105° F.; T3=115° F.; and Lr=0.98. Equation (13) gives T1 e=98° F.; T2 e=103° F.; and T3 e=113° F.

Step 905 calculates the average effective temperature Ta as the mean of T3 e and T2 e, so that Ta=108° F. Step 906 calculates the available volume of water Ca as 2/3Ct, i.e., 50 gallons. Using these figures, equation (15) becomes:

${Ma} = {\frac{50\left( {108 - 50} \right)}{2.5\left( {100 - 50} \right)} = {23.2\mspace{14mu} {minutes}}}$

In a display step 908, display unit 34 shows the available time, Ma, that tank 24 can deliver water, so that the temperature at faucet 26 is Tu.

Returning to comparison 904, if all of T1 e, T2 e, T3 e are less than Tu, the processing unit continues to display step 909. In display step 909, display unit 34 shows that there is no available water, i.e., that Ma=0.

In a second comparison 910, which follows from steps 908 and 909, processing unit 102 uses display 34 to ask if the user wants to heat the water in tank 24. If the return from the second comparison is negative, i.e., the water is not to be heated in the tank, the process illustrated by the flow chart ends.

If the return from the second comparison is positive, the processing unit continues to a maximum time step 911. Step 911 is substantially the same as step 610, so that the processing unit assumes that all the water in tank 24 is raised to the maximum set temperature Ts of the tank, and uses equation (4) to calculate Mm.

A user step 912 is substantially the same as user step 611. The user operates input device 32 to provide processing unit 102 with a length of time required, Mr, for mixed water at temperature Tu.

In a third comparison 913 processing unit 102 compares Mr and Mm. (Comparison 913 is generally the same as comparison 612.) If Mr≦Mm the flow chart continues to a required temperature calculation step 914. If Mr>Mm the flow chart continues to an activation step 918.

In step 914 the processing unit, using required-temperature module 715, decides which heaters, 120, 321, and/or 322 are to be activated, and to what temperatures, as measured by sensors 114, 315, and 316, sections V1, V2, and/or V3 are to be raised. The required temperatures of sections V1, V2, and V3 are respectively termed Tr1, Tr2, and Tr3.

FIGS. 8A-8N illustrate a flow chart followed by processing unit 102 in implementing step 914 and an activation step 915 described below, according to an embodiment of the present invention. The decisions are based on the processing unit analyzing the heat content of the water in the sections of the tank in a sequential manner, starting from an analysis of the top third of the tank, and applying the law of conservation of energy to determine to what temperature different sections of the tank are to be heated. If the processing unit determines that the top third of the tank is not able to meet the required Mr, the unit then analyzes the top two sections. Similarly, if processing unit 102 determines that the top two thirds of the tank are not able to meet the required Mr, the unit analyzes all three sections.

The analysis also assumes that no section of the tank may be heated to more than the set temperature Ts. Furthermore, the analysis assumes that no given section is heated to a temperature that is higher than the temperature of a section above the given section. Thus, in no case is Tr1>Tr2, and in no case is Tr2>Tr3.

In the flow chart, a comparison which is identified by a numeral without a letter suffix typically refers to a comparison made by the processing unit to evaluate if a given section of the tank is able to supply the needed value of Mr. If the comparison is valid, subsequent steps are identified by the comparison numeral with a letter appended.

In a comparison 800, to check the top third of the tank, unit 102 checks if the expression (Mr≦(1/3)Ct/Fr and T3·Lr<Tu) is valid. If it is, so that the top third is able to supply Mr, then in an activation step 800A, the unit activates heater 322 until Tr3≧Tu/Lr. If the expression is not valid, unit 102 analyzes the top two thirds of the tank, beginning with a comparison 802, to see if the top two thirds are able to supply Mr.

Comparison 802 checks if the expression

$\quad\begin{pmatrix} {{\left( {1/3} \right){{Ct}/{Fr}}} < {Mr} \leq {\left( {2/3} \right){{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{T\; {3 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} < {{Mm}/3}} \end{pmatrix}$

is valid. If it is, unit 102 first calculates a value for Tr3 in a step 802A:

${{Tr}\; 3} = \frac{{{Mr} \cdot {Fr} \cdot \left( {{Tu} - {Tc}} \right)} + {\left( {1/3} \right){{Ct} \cdot {Tc}}}}{\left( {1/3} \right){{Ct} \cdot {Lr}}}$

and then in a comparison 802B the unit checks if Tr3−T3≦2Tu/Lr−T3−T2 is valid. Comparison 802B is written in this form, i.e., not in a simpler equivalent form Tr3≦2Tu/Lr−T2, as are other temperature comparisons of the flow chart, to indicate that the capacities of sections of the tank are being compared. In this case the capacity of the top section is compared to the capacity of the top two sections.

If comparison 802B is valid (so that only the top section needs to be heated to supply Mr), then in an activation step 802C heater 322 is activated until Tr3 is reached. If the comparison is not valid (so that the two top sections need to be heated), then in an activation step 802D heater 322 is activated until Tr3≧Tu/Lr and heater 321 is activated until Tr2≧Tu/Lr. If the expression of comparison 802 is not valid, unit 102 continues to a comparison 804.

Comparison 804 checks if the expression

$\quad\begin{pmatrix} {{\left( {1/3} \right){{Ct}/{Fr}}} < {Mr} \leq {\left( {2/3} \right){{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{2{Tu}} > {T\; {3 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} < {{Mm}/3}} \end{pmatrix}$

is valid. If it is, unit 102 calculates a value for Tr3 in a step 804A, as in step 802A, and then in a comparison 804B the unit checks if Tr3−T3≦Tu/Lr−T2 is valid. If the comparison is valid, then in an activation step 804C heater 322 is activated until Tr3 is reached. If the comparison is not valid, then in an activation step 804D heater 321 is activated until Tr2≧Tu/Lr. If the expression of comparison 804 is not valid, unit 102 continues to a comparison 806.

Comparison 806 checks if the expression

$\quad\begin{pmatrix} {{\left( {1/3} \right){{Ct}/{Fr}}} < {Mr} \leq {\left( {2/3} \right){{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{T\; {3 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} = {{Mm}/3}} \end{pmatrix}$

is valid. If it is, a comparison 806A, Ts·Lr−T3·Lr≦2Tu/Lr−T3−T2, is checked for validity. If comparison 806A is valid, then in an activation step 806B, heater 322 is activated until Tr3=Ts. If comparison 806A is not valid, then in an activation step 806C, heater 321 is activated until Tr2≧Tu/Lr. If the expression of comparison 806 is not valid, unit 102 continues to a comparison 808.

Comparison 808 checks if the expression

$\quad\begin{pmatrix} {{\left( {1/3} \right){{Ct}/{Fr}}} < {Mr} \leq {\left( {2/3} \right){{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{2{Tu}} > {T\; {3 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} = {{Mm}/3}} \end{pmatrix}$

is valid. If it is, a comparison 808A, Ts·Lr−T3·Lr≦Tu/Lr−T2, is checked for validity. If comparison 808A is valid, then in an activation step 808B, heater 322 is activated until Tr3=Ts. If comparison 808A is not valid, then in an activation step 808C, heater 321 is activated until Tr2≧Tu/Lr. If the expression of comparison 808 is not valid, unit 102 continues to a comparison 810.

Comparison 810 checks if the expression

$\quad\begin{pmatrix} {{\left( {1/3} \right){{Ct}/{Fr}}} < {Mr} \leq {\left( {2/3} \right){{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{T\; {3 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} > {{Mm}/3}} \end{pmatrix}$

is valid. If it is, then in an activation step 810A, heater 322 is activated until Tr3≧Tu/Lr and heater 321 is also activated until Tr2≧Tu/Lr. If the expression of comparison 810 is not valid, unit 102 continues to a comparison 812.

Comparison 812 checks if the expression

$\quad\begin{pmatrix} {{\left( {1/3} \right){{Ct}/{Fr}}} < {Mr} \leq {\left( {2/3} \right){{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{2{Tu}} > {T\; {3 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} > {{Mm}/3}} \end{pmatrix}$

is valid. If it is, then in an activation step 812A, heater 321 is activated until Tr2≧Tu/Lr. If the comparison 812 is not valid, unit 102 continues to a comparison 814.

Comparisons 802 to 812 check if the top two thirds of the tank can supply Mr. If none of the comparisons have returned a positive answer, the processing unit continues by checking the remainder of the tank, starting at comparison 814.

Comparison 814 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right) \cdot {{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{T\; {3 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} < {{Mm}/3}} \end{pmatrix}$

is valid. If it is, unit 102 calculates a value for Tr3 in a step 814A:

${{{Tr}\; 3} = \frac{{{Mr} \cdot {Fr} \cdot \left( {{Tu} - {Tc}} \right)} + {\left( {1/3} \right){{Ct} \cdot {Tc}}}}{\left( {1/3} \right){{Ct} \cdot {Lr}}}},$

and then in a comparison 814B the unit checks if Tr3−T3≦3Tu/Lr−T3−T2−T1 is valid. If comparison 814B is valid, heater 322 is activated until Tr3 is reached. If comparison 814B is not valid, then unit 102 calculates a new value for Tr3, and the same value for Tr2, in a step 814D. The notation Tr2,3 is used herein to indicate Tr2 or Tr3 when the two values are the same. In step 814D the processing unit calculates the value for Tr2,3 as:

${{Tr}\; 2},{3 = {\frac{{{Mr} \cdot {Fr} \cdot \left( {{Tu} - {Tc}} \right)} + {\left( {2/3} \right){{Ct} \cdot {Tc}}}}{\left( {1/3} \right){{Ct} \cdot {Lr}}}.}}$

In a comparison 814E the processing unit checks if 2Tr2,3−T3−T2≦3Tu/Lr−T3−T2−T1 is valid. If it is valid, then in an activation step 814F heaters 322 and 321 are activated until Tr2,3 is reached. If comparison 814E is not valid, then in an activation step 814G heater 322 is activated until Tr3≧Tu/Lr, heater 321 is activated until Tr2≧Tu/Lr, and heater 120 is activated until Tr1≧Tu/Lr.

If comparison 814 is not valid, the processing unit continues to a comparison 816.

Comparison 816 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right) \cdot {{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{2{Tu}} > {T\; {3 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} < {{Mm}/3}} \end{pmatrix}$

is valid. If it is, unit 102 calculates a value for Tr3 in a step 816A:

${{{Tr}\; 3} = \frac{{{Mr} \cdot {Fr} \cdot \left( {{Tu} - {Tc}} \right)} + {\left( {1/3} \right){{Ct} \cdot {Tc}}}}{\left( {1/3} \right){{Ct} \cdot {Lr}}}},$

and then in a comparison 816B the unit checks if Tr3−T3≦2Tu/Lr−T2−T1 is valid.

If comparison 816B is valid, in an activation step 816C heater 322 is activated until Tr3 is reached. If comparison 816B is not valid, unit 102 sets the value of Tr2,3 to the value given above for step 814D, and proceeds to a comparison 816E. In comparison 816E the processing unit checks if 2Tr2,3−T3−T2≦2Tu/Lr−T2−T1 is valid. If the comparison is valid, then in an activation step 816F heaters 322 and 321 are activated until TR2,3 is reached. If comparison 816E is invalid, then in an activation step 816G heater 321 is activated until Tr2≧Tu/Lr and heater 120 is activated until Tr1≧Tu/Lr.

If comparison 816 is invalid, the processing unit continues to a comparison 818.

Comparison 818 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right){{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{2{Tu}} > {T\; {3 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} < {{Mm}/3}} \end{pmatrix}$

is valid. If it is valid, then unit 102 calculates a value for Tr3 in a step 818A:

${{{Tr}\; 3} = \frac{{{Mr} \cdot {Fr} \cdot \left( {{Tu} - {Tc}} \right)} + {\left( {1/3} \right){{Ct} \cdot {Tc}}}}{\left( {1/3} \right){{Ct} \cdot {Lr}}}},$

and then in a comparison 818B the unit checks if Tr3−T3≦Tu/Lr−T1 is valid. If comparison 818B is valid then in a step 818C heater 322 is activated until Tr3 is reached. If comparison 818B is not valid, then unit 102 calculates the value of Tr2,3 according to the value given above for step 814D, and proceeds to a comparison 818E. In comparison 818E the processing unit checks if 2Tr2,3−T3−T2≦Tu/Lr−T1 is valid. If the comparison is valid, then in an activation step 818F heaters 322 and 321 are activated until Tr2,3 is reached. If comparison 818E is invalid, then in an activation step 818G heater 120 is activated until Tr1≧Tu/Lr.

If comparison 818 is invalid, processing unit 102 continues to a comparison 820.

Comparison 820 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right) \cdot {{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{T\; {3 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} = {{Mm}/3}} \end{pmatrix}$

is valid. If the expression is valid, then in a comparison 820A unit 102 evaluates if Ts·Lr−T3·Lr≦3Tu/Lr−T3−T2−T1 is valid. If the return is positive, then in an activation step 82B unit 102 activates heater 322 until Tr3=Ts. If the return from comparison 320A is negative, then in a step 820C the processing unit calculates the value of Tr2,3 according to the value given above for step 814D, and proceeds to a comparison 820D.

Comparison 820D checks if 2Tr2,3−T3≦T2≦3Tu/Lr−T3−T2−T1 is valid. If the comparison is valid, then heaters 322 and 321 are activated until Tr2,3 is reached. If the comparison is invalid, then heaters 322, 321, and 120 are activated until Tr3≧Tu/Lr, Tr2≧Tu/Lr, and Tr1≧Tu/Lr.

If comparison 820 is invalid, processing unit 102 continues to a comparison 822.

Comparison 822 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right){{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{2{Tu}} > {T\; {3 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} = {{Mm}/3}} \end{pmatrix}$

is valid. If the expression is valid, then in a comparison 822A, the processing unit checks if Ts·Lr−T3·Lr≦2Tu/Lr−T2−T1 is valid. If it is valid, then in an activation step 822B heater 322 is activated until Tr3=Ts. If comparison 822A is invalid, then in a step 822C the processing unit calculates the value of Tr2,3 according to the expression given above for step 814D, and proceeds to a comparison 822D.

Comparison 822D checks if 2Tr2,3−T3−T2≦2Tu/Lr−T2−T1 is valid. If the comparison is valid, then in an activation step 822E heaters 322 and 321 are activated until Tr2,3 is reached. If the comparison is invalid, then in an activation step 822F heaters 321 and 120 are activated until Tr2≧Tu/Lr and Tr1≧Tu/Lr.

If comparison 822 is invalid, processing unit 102 continues to a comparison 824.

Comparison 824 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right){{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{2{Tu}} > {T\; {3 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} = {{Mm}/3}} \end{pmatrix}$

is valid. If the expression is valid, then in a comparison 824A, the processing unit checks if the comparison Ts·Lr−T3·Lr≦Tu/Lr−T1 is valid. If comparison 824A is valid, then in an activation step 824B heater 322 is activated until Tr3=Ts. If comparison 824A is invalid, then in a step 824C the processing unit calculates Tr2,3 according to the expression given above for step 814D, and proceeds to a comparison 824D.

Comparison 824D checks if 2Tr2,3−T3−T2≦Tu/Lr−T1 is valid. If the comparison is valid, then in an activation step 824E heaters 322 and 321 are activated until Tr2,3 is reached. If the comparison is invalid, then in an activation step 824F heater 120 is activated until Tr1≧Tu/Lr.

If comparison 824 is invalid, processing unit 102 continues to a comparison 826.

Comparison 826 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right) \cdot {{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{T\; {3 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{{Mm}/3} < {Mr} < {2{{Mm}/3}}} \end{pmatrix}$

is valid. If comparison 826 is valid, then in a step 826A the processing unit calculates Tr2,3 according to the expression given above for step 814D, and proceeds to a comparison 826B.

Comparison 826B checks if 2Tr2,3−T3−T2≦3Tu/Lr−T3−T2−T1 is valid. If the comparison is valid, then in an activation step 826C heaters 322 and 321 are activated until Tr2,3 is reached. If the comparison is invalid, then in an activation step 826D heaters 322, 321, and 120 are activated until Tr3≧Tu/Lr, Tr2≧Tu/Lr, and Tr1≧Tu/Lr.

If comparison 826 is invalid, processing unit 102 continues to a comparison 828.

Comparison 828 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right) \cdot {{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{2{Tu}} > {T\; {3 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{{Mm}/3} < {Mr} < {2{{Mm}/3}}} \end{pmatrix}$

is valid. If comparison 826 is valid, then in a step 828A the processing unit calculates Tr2,3 according to the expression given above for step 814D, and proceeds to a comparison 828B.

Comparison 828B checks if 2Tr2,3−T3−T2≦2Tu/Lr−T2−T1 is valid. If the comparison is valid, then in an activation step 828C heaters 322 and 321 are activated until Tr2,3 is reached. If the comparison is invalid, then in an activation step 828D heaters 321 and 120 are activated until Tr2≧Tu/Lr and Tr1≧Tu/Lr.

If comparison 828 is invalid, processing unit 102 continues to a comparison 830.

Comparison 830 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right) \cdot {{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{2{Tu}} > {T\; {3 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{{Mm}/3} < {Mr} < {2{{Mm}/3}}} \end{pmatrix}$

is valid. If comparison 826 is valid, then in a step 830A the processing unit calculates Tr2,3 according to the expression given above for step 814D, and proceeds to a comparison 830B.

Comparison 830B checks if 2Tr2,3−T3−T2≦2Tu/Lr−T1 is valid. If the comparison is valid, then in an activation step 830C heaters 322 and 321 are activated until Tr2,3 is reached. If the comparison is invalid, then in an activation step 830D heater 120 is activated until Tr1≧Tu/Lr.

If comparison 830 is invalid, processing unit 102 continues to a comparison 832.

Comparison 832 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right) \cdot {{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{T\; {3 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} = {2{{Mm}/3}}} \end{pmatrix}$

is valid. If comparison 832 is valid, the processing unit checks if a comparison 832A: 2Ts·Lr−T3·Lr−T2·Lr≦3Tu/Lr−T3−T2−T1 is valid. If comparison 832A is valid, then in an activation step 832B heaters 322 and 321 are activated until Tr3=Ts and Tr2=Ts. If comparison 832A is not valid, then in an activation step 832C heaters 322, 321, and 120 are activated until Tr3≧Tu/Lr, Tr2≧Tu/Lr, and Tr1≧Tu/Lr.

If comparison 832 is invalid, processing unit 102 continues to a comparison 834.

Comparison 834 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right) \cdot {{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{2{Tu}} > {T\; {3 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} = {2{{Mm}/3}}} \end{pmatrix}$

is valid. If comparison 834 is valid, the processing unit checks if a comparison 834A: 2Ts·Lr−T3·Lr−T2·Lr≦2Tu/Lr−T2−T1 is valid. If comparison 834A is valid, then in an activation step 834B heaters 322 and 321 are activated until Tr3=Ts and Tr2=Ts. If comparison 834A is not valid, then in an activation step 834C heaters 322, 321, and 120 are activated until Tr3≧Tu/Lr, Tr2≧Tu/Lr, and Tr1≧Tu/Lr.

If comparison 834 is not valid, the processing unit continues to a comparison 836.

Comparison 836 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right) \cdot {{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{2{Tu}} > {T\; {3 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} = {2{{Mm}/3}}} \end{pmatrix}$

is valid. If comparison 836 is valid, the processing unit checks if a comparison 836A: 2Ts·Lr−T3·Lr−T2·Lr≦Tu/Lr−T1 is valid. If comparison 836A is valid, then in an activation step 836B heaters 322 and 321 are activated until Tr3=Ts and Tr2=Ts. If comparison 836A is not valid, then in an activation step 836C heaters 322, 321, and 120 are activated until Tr3≧Tu/Lr, Tr2≧Tu/Lr, and Tr1≧Tu/Lr.

If comparison 836 is not valid, the processing unit continues to a comparison 838.

Comparison 838 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right) \cdot {{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{T\; {3 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} > {2{{Mm}/3}}} \end{pmatrix}$

is valid. If the comparison is valid, then in an activation step 838A heaters 322, 321, and 120 are activated until Tr3≧Tu/Lr, Tr2≧Tu/Lr, and Tr1≧Tu/Lr. If the comparison is invalid, the processing unit continues to a comparison 840.

Comparison 840 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right) \cdot {{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{2{Tu}} > {T\; {3 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} > {2{{Mm}/3}}} \end{pmatrix}$

is valid. If the comparison is valid, then in an activation step 840A heaters 321 and 120 are activated until Tr2>Tu/Lr and Tr1≧Tu/Lr. If the comparison is invalid, the processing unit continues to a comparison 842.

Comparison 842 checks if the expression

$\quad\begin{pmatrix} {{\left( {2/3} \right) \cdot {{Ct}/{Fr}}} < {Mr} \leq {{{Ct}/{Fr}}\mspace{14mu} {and}}} \\ {{2{Tu}} > {T\; {3 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {2 \cdot {Lr}}} \geq {{Tu}\mspace{14mu} {and}\mspace{14mu} T\; {1 \cdot {Lr}}} < {{Tu}\mspace{14mu} {and}}} \\ {{Mr} > {2{{Mm}/3}}} \end{pmatrix}$

is valid. If the comparison is valid, then in an activation step 842A heater 120 is activated until Tr1≧Tu/Lr. If the comparison is invalid, the processing unit continues to a comparison 844.

Comparison 844 checks if (Mm>Mr>Ct/Fr). If the comparison is valid, then in a step 844A the processing unit calculates an average temperature Tr to which all three sections of the tank may be raised. The average temperature for all three sections is also herein referred to as Avg.(Tr1, Tr2, Tr3), but should not be confused as being determined by taking the average of the temperatures sampled by the temperature sensors. In step 844A Tr is given by:

${Tr} = {{{Avg}.\left( {{{Tr}\; 1},{{Tr}\; 2},{{Tr}\; 3}} \right)} = {\frac{{{Mr} \cdot {Fr} \cdot \left( {{Tu} - {Tc}} \right)} + {{Ct} \cdot {Tc}}}{{Ct} \cdot {Lr}}.}}$

In a comparison 844B the processing unit checks if the comparison (T3<Tr and T2<Tr and T1<Tr) is valid. If it is, then in an activation step 844C heaters 322, 321, and 120 are activated until T3≧Tr, T2≧Tr, and T1≧Tr. If comparison 844B is invalid, unit 102 proceeds to a comparison 844D: (T3>Tr and T2<Tr and T1<Tr).

If comparison 844D is valid, the processing unit calculates an average temperature for the lower two sections of the tank in a step 844E. The average temperature for the lower two sections is also referred to as Avg.(Tr1, Tr2), and should not be confused as being determined from the average of the temperatures sampled by the lower two sensors. In step 844E Avg.(Tr1, Tr2) is calculated according to the expression:

${{{Avg}.\left( {{{Tr}\; 1},{{Tr}\; 2}} \right)} = {{Tr} - \frac{{T\; 3} - {Tr}}{2}}},$

where Tr is as calculated in step 844A.

After step 844E, unit 102 checks in a comparison 844F if Avg.(Tr1, Tr2)>T2. If the comparison is valid, then in an activation step 844G unit 102 activates heater 321 until T2≧Avg.(Tr1, Tr2), and activates heater 120 until T1≧Avg.(Tr1, Tr2). If comparison 844F is not valid, then in an activation step 844H unit 102 activates heater 120 until T1≧2 Avg.(Tr1, Tr2)−T2.

Returning to comparison 844D, if the comparison is invalid, then the processing unit performs another comparison 844I: (T3>Tr and T2>Tr and T1<Tr). If the comparison is valid, then in an activation step 844J heater 120 is activated until T1≧3Tr−T3−T2. If comparison 844I is invalid, then Mr=Mm, i.e., the required mixed water is equal to the maximum mixed water capacity of the tank, so that in an activation step 844K heaters 322, 321 and 120 are activated until Tr1=Tr2=Tr3=Ts.

Returning to comparison 844, if the comparison is invalid, then Mr=Mm and the processing unit proceeds to activation step 844K.

In some embodiments, sensor 317 and valve 118 are installed in system 300. In this case unit 102 may measure the temperature (T4) of water exiting tank 24 using sensor 317. If

${{T\; 4} < \frac{Tu}{Lr}},$

then unit 102 may operate valve 118 to prevent water from exiting the tank.

In some embodiments, flow sensor 130 and flow rate module 517 are present in system 300. If so, the sensor and module function substantially as described above for system 20, enabling, for example, a real time display of a period for which water at temperature Tu is available.

Returning to the flow chart of FIG. 7, following from the completion of step 914, in an activation step 915 heaters 120, 321, and/or 322 are activated as determined in the flow chart of FIGS. 8A-8N.

In a deactivation step 916, when the conditions determined in the flow chart of FIGS. 8A-8N have been met, heaters that have been activated in step 915 are deactivated.

In a display step 917, once the temperatures determined in step 914 have been reached, display 34 indicates to the user that the water in tank 24 has been sufficiently heated to satisfy the user's requirements, i.e., that there is sufficient hot water for faucet 26 to supply water to the user at temperature Te (Tu·Lr) for a required time Mr. The flow chart then ends.

Except as described below, steps 918, 919, 920, 921, 922, 923 and 924 are generally similar respectively to steps 617, 618, 619, 620, 621, 622, and 623 (FIG. 4). In step 918, depending on the difference between Mr and Mm, one or more of heaters 120, 321, and 322 are activated. Similarly, in steps 923 and 924, depending on the value of Mh (determined in step 922) heaters 120, 321, and/or 322 are activated and deactivated according to whether T1<Ts and/or T2<Ts and/or T3<Ts.

The embodiments described above have considered one user using a water supply system. However, it will be understood that the water supply system may be configured, mutatis mutandis, to be used by two or more users, where there is a common time period wherein the two or more users use the system simultaneously.

Thus, in the case of exemplary shower system 300 described above (FIGS. 1, 5A, 5B, 6), such a configuration typically requires replication of shower 22, and elements within the shower comprising faucet 26, control unit 30, data input device 32, data output device 34, and incorporation of flow sensor 130. Typically, the multiple control units are configured to communicate with each other. In the following description, as applicable, items of the water supply system are differentiated by appending a letter to the identifying numeral of the item, for example, shower 22A, shower 22B, . . . .

For example, a user A may at 9 a.m. require a supply of water at 105° F. for 20 minutes in a shower 22A, and a user B may at 9:10 a.m. require a supply of water at 98° F. for 15 minutes in a shower 22B. Both users input their requirements into their respective control units 30A, 30B, and begin to use their faucets 26A, 26B so as to receive hot water simultaneously from 9:10 a.m. During operation of showers 22A and/or 22B, respective control units 30A and 30B communicate between themselves, and with sensors 130A and 130B, in order to determine requirements of user A, user B, and amounts of water that have been used by each user. From the determinations, the control units are able to perform substantially the same processes described above with respect to the flow chart of FIG. 7.

Alternatively or additionally, not all of the elements within a particular shower may be replicated. For example, a single control unit 30S, having a functionality generally similar to control unit 30, may be coupled to a group of showers 22A, 22B, . . . , and single control unit 30S may be typically further configured to be accessible to users A, B, . . . . The requirements of each user may be entered into the single control unit, typically, but not necessarily, by the users themselves operating the unit. Control unit 30S may be configured to accept differentiating identifying data, that differentiates between the requirements of the different users, that is entered into the control unit via a data input device 32S. The differentiating identifying data typically comprises an identifier of respective users A, B, . . . , and/or an identifier of respective showers 22A, 22B, . . . . From the requirements, control unit 30S is able to perform substantially the same processes described above with respect to the flow chart of FIG. 7.

In the case of exemplary shower system 20 (FIGS. 1, 2A, 2B, 3), the replication required for two or more users is substantially as described above for system 300. As for system 300, system 20 may be configured to operate with multiple communicating control units, or with a single control unit that differentiates between requirements of different users. In the reconfiguration of system 20 to accommodate two or more users, the one or more control units operating the reconfigured system are typically configured to mix the water in hot water tank 24, using pump 127, when a first user starts to operate the reconfigured system, and not to mix the water until the first user's requirements have been met.

Thus, if one or more second users input respective requirements while the first user is still receiving water from the tank, as determined by a flow sensor 130 for the first user, the one or more control units add the new requirements to those already input for the first user, without further mixing of the water in tank 24. The one or more control units then determine whether or not the new requirements can be met from the water in tank 24, and provide corresponding outputs to the one or more second users. The outputs provided typically comprise respective available times for the one or more second users, or that a given requirement cannot be met.

In the latter case, i.e., wherein there is a situation of no availability, the one or more control units may be configured to calculate a required heating time, using a method generally similar to that described above with reference to equations (9) and (12), and display such a time to users whose requirements cannot be met.

It will be appreciated that the embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and sub-combinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art. 

1. A method, comprising: receiving an instruction from a user of a hot water tank indicating a target temperature and a duration of a supply of water; in response to the instruction, mixing water at multiple different temperatures within the hot water tank so as to form mixed water therein; measuring an actual temperature of the mixed water in order to make a determination of whether the mixed water will satisfy the instruction; and activating a heater to heat the mixed water responsively to the determination. 2-9. (canceled)
 10. Apparatus, comprising: a hot water tank; a first vertical array of heaters deployed within the hot water tank; a second vertical array of temperature sensors deployed within the hot water tank; and a control unit which is configured: to receive an instruction from a user of the hot water tank indicating a requirement of a supply of water, to receive signals from the temperature sensors representative of respective temperatures thereof, and to activate at least one of the heaters in response to the signals and the requirement.
 11. The apparatus according to claim 10, wherein the first vertical array of heaters are located according to a first vertical distribution and wherein the second vertical array of sensors are located according to a second vertical distribution.
 12. (canceled)
 13. (canceled)
 14. The apparatus according to claim 11, wherein the second vertical distribution is different from the first vertical distribution.
 15. The apparatus according to claim 10, wherein the control unit is configured to activate the at least one of the heaters in response to evaluating a heat loss factor of a temperature drop from the hot water tank to a water outlet supplying the user.
 16. The apparatus according to claim 10, wherein the control unit is configured to activate the at least one of the heaters in response to measuring a temperature of a cold water supply to the user.
 17. The apparatus according to claim 10, wherein the control unit is configured to activate the at least one of the heaters in response to receiving a positive response to a query to the user whether water within the hot water tank is to be heated.
 18. The apparatus according to claim 10, wherein the instruction is indicative of a temperature and a volume of the supply of water.
 19. The apparatus according to claim 10, wherein the control unit is configured to activate the at least one of the heaters in response to analyzing sequentially heat contents of respective sections of the tank defined by the first vertical array.
 20. The apparatus according to claim 10, wherein the first vertical array defines respective sections of the tank, and wherein the control unit is configured to activate the at least one of the heaters in response to maintaining that no given section is heated to a first temperature that is higher than a second temperature of a further section above the given section.
 21. The apparatus according to claim 10, wherein receiving the instruction comprises determining that a maximum heat capacity of water in the tank is insufficient for satisfying the instruction, and in response determining a length of time required to heat water entering the tank. 22-30. (canceled)
 31. A method, comprising: deploying a first vertical array of heaters within a hot water tank; deploying a second vertical array of temperature sensors within the hot water tank; and configuring a control unit: to receive an instruction from a user of the hot water tank indicating a requirement of a supply of water, to receive signals from the temperature sensors representative of respective temperatures thereof, and to activate at least one of the heaters in response to the signals and the requirement.
 32. The method according to claim 31, and comprising locating the first vertical array of heaters according to a first vertical distribution and locating the second vertical array of sensors according to a second vertical distribution.
 33. (canceled)
 34. (canceled)
 35. The method according to claim 32, wherein the second vertical distribution is different from the first vertical distribution.
 36. The method according to claim 31, wherein the control unit is configured to activate the at least one of the heaters in response to evaluating a heat loss factor of a temperature drop from the hot water tank to a water outlet supplying the user.
 37. The method according to claim 31, wherein the control unit is configured to activate the at least one of the heaters in response to measuring a temperature of a cold water supply to the user.
 38. The method according to claim 31, wherein the control unit is configured to activate the at least one of the heaters in response to receiving a positive response to a query to the user whether water within the hot water tank is to be heated.
 39. The method according to claim 31, wherein the instruction is indicative of a temperature and a duration of the supply of water.
 40. The method according to claim 31, wherein the control unit is configured to activate the at least one of the heaters in response to analyzing sequentially heat contents of respective sections of the tank defined by the first vertical array.
 41. The method according to claim 31, wherein the first vertical array defines respective sections of the tank, and wherein the control unit is configured to activate the at least one of the heaters in response to maintaining that no given section is heated to a first temperature that is higher than a second temperature of a further section above the given section. 42-46. (canceled) 